# Converter of signed binary two's complement: converting to decimal system (base ten) integer numbers

## Latest binary numbers in two's complement representation converted to signed integers in decimal system (base ten)

 0000 0000 1001 1010 1000 1010 1010 0110 1001 0000 1010 1010 1000 1110 1000 1110 = 43,499,594,409,741,966 May 24 14:59 UTC (GMT) 1111 0001 = -15 May 24 14:57 UTC (GMT) 1111 1010 = -6 May 24 14:56 UTC (GMT) 1111 1111 1111 1000 = -8 May 24 14:55 UTC (GMT) 0000 1100 1110 0101 = 3,301 May 24 14:53 UTC (GMT) 1001 0010 0101 0000 = -28,080 May 24 14:52 UTC (GMT) 0000 0000 0000 0000 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 = 1,099,511,627,775 May 24 14:52 UTC (GMT) 1001 0101 0101 0101 = -27,307 May 24 14:52 UTC (GMT) 1111 1011 1111 1110 = -1,026 May 24 14:51 UTC (GMT) 1111 1111 1100 1011 = -53 May 24 14:51 UTC (GMT) 1011 0011 = -77 May 24 14:45 UTC (GMT) 0100 0110 1111 0011 1110 0111 0000 0000 = 1,190,389,504 May 24 14:42 UTC (GMT) 0001 = 1 May 24 14:39 UTC (GMT) All the converted signed binary two's complement numbers

## How to convert signed binary numbers in two's complement representation from binary system to decimal

### To understand how to convert a signed binary number in two's complement representation from the binary system to decimal (base ten), the easiest way is to do it by an example - convert binary, 1101 1110, to base ten:

• In a signed binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
• Get the signed binary representation in one's complement, subtract 1 from the initial number:
1101 1110 - 1 = 1101 1101
• Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1101 1101) = 0010 0010
• Write bellow the positive binary number representation in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 by exactly one unit:
•  powers of 2: 7 6 5 4 3 2 1 0 digits: 0 0 1 0 0 0 1 0
• Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up: